Subgroups — C₇×#36631 #13213847

Order 1792.

2670 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#529	C₂	1	2	yes	maximal, complemented
2	C₇×#2861	C₂	1	2	yes	maximal, complemented
3	C₇×#2860	C₂	1	4	yes	maximal, complemented
4	C₇×#2859	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2858	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#2857	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#2856	C₂	1	1	yes	maximal, characteristic
8	C₇×#2854	C₂	1	4	yes	maximal, complemented
9	C₇×#2850	C₂	1	2	yes	maximal, complemented
10	C₄×C₇×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₇×#127	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₇×#124	C₂	1	2	yes	maximal, complemented
13	C₄×C₇×#121	C₂	1	4	yes	maximal, complemented
14	C₇×#2293	C₂	1	4	yes	maximal, complemented
15	C₂×C₄³×C₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₇×#127	C₂²	1	1	yes	characteristic
18	C₇×#529	—	2	16	no	—
19	C₂×C₇×#126	C₂²	1	4	yes	—
20	C₂×C₇×#125	C₂²	1	2	yes	—
21	C₂×C₇×#124	C₂²	1	2	yes	—
22	C₂×C₇×#124	C₂²	1	2	yes	—
23	C₂×C₇×#123	C₂²	1	4	yes	—
24	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
25	C₂×C₇×#121	C₂²	1	2	yes	—
26	C₂×C₇×#121	C₂²	1	4	yes	—
27	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
28	C₂×C₄×C₇×D₄	C₂²	1	4	yes	—
29	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
30	C₂×C₄×C₇×D₄	C₂²	1	4	yes	—
31	C₂×C₇×#117	C₂²	1	4	yes	—
32	C₂²×C₄²×C₇	C₂²	1	2	yes	—
33	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
34	C₂²×C₄²×C₇	C₂²	1	2	yes	—
35	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
37	C₇×#391	C₂²	1	2	yes	—
38	C₇×#391	C₂²	1	2	yes	—
39	C₇×#390	C₂²	1	4	yes	—
40	C₇×#390	C₂²	1	4	yes	—
41	C₇×#390	C₂²	1	4	yes	—
42	C₇×#390	C₂²	1	2	yes	—
43	C₇×#390	C₂²	1	2	yes	—
44	C₇×#390	C₂²	1	4	yes	—
45	C₇×#389	C₂²	1	4	yes	—
46	C₇×#389	C₂²	1	4	yes	—
47	C₇×#389	C₂²	1	4	yes	—
48	C₇×#389	C₂²	1	4	yes	—
49	C₇×#388	C₂²	1	8	yes	—
50	C₇×#388	C₂²	1	8	yes	—
51	C₇×#388	C₂²	1	8	yes	—
52	C₇×#388	C₂²	1	8	yes	—
53	C₇×#386	C₂²	1	8	yes	—
54	C₇×#384	C₂²	1	1	yes	characteristic
55	C₇×#384	C₂²	1	1	yes	characteristic
56	C₇×#382	C₂²	1	2	yes	—
57	C₇×#380	C₂²	1	4	yes	—
58	C₄×C₇×C₄⋊C₄	C₂²	1	4	yes	—
59	C₄×C₇×C₂²⋊C₄	C₂²	1	8	yes	—
60	C₄³×C₇	C₂²	1	2	yes	—
61	C₄³×C₇	C₂²	1	1	yes	characteristic
62	C₄³×C₇	C₂²	1	1	yes	characteristic
63	C₄³×C₇	C₂²	1	1	yes	characteristic
64	C₄³×C₇	C₂²	1	2	yes	—
65	C₄³×C₇	C₂²	1	1	yes	characteristic
66	#36631	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
67	C₂²×C₇×Q₈	C₂³	1	2	yes	—
68	C₂²×C₇×D₄	C₂³	1	4	yes	—
69	C₂²×C₇×D₄	C₂³	1	2	yes	—
70	C₂²×C₇×D₄	C₂³	1	4	yes	—
71	C₂³×C₄×C₇	C₂³	1	2	yes	—
72	C₂³×C₄×C₇	C₂³	1	4	yes	—
73	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₇	C₂³	1	2	yes	—
77	C₇×C₄⋊Q₈	—	2	4	no	—
78	C₇×#127	—	2	4	no	—
79	C₇×#126	—	2	16	no	—
80	C₇×#125	—	2	8	no	—
81	C₇×#124	—	2	8	no	—
82	C₇×#124	—	2	8	no	—
83	C₇×#123	—	2	16	no	—
84	C₇×C₂²⋊Q₈	—	2	8	no	—
85	C₇×#121	—	2	8	no	—
86	C₇×#121	—	2	16	no	—
87	C₄×C₇×Q₈	—	2	8	no	—
88	C₄×C₇×D₄	—	2	16	no	—
89	C₄×C₇×D₄	—	2	8	no	—
90	C₄×C₇×D₄	—	2	16	no	—
91	C₇×#117	—	2	16	no	—
92	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
93	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
94	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
95	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
96	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
97	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
98	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
99	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
100	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
101	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
102	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
103	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
104	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
105	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
106	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
107	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
108	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
109	C₂×C₄²×C₇	—	2	8	no	—
110	C₂×C₄²×C₇	—	2	8	no	—
111	C₂×C₄²×C₇	—	2	4	no	—
112	C₂×C₄²×C₇	—	2	4	no	—
113	C₂×C₄²×C₇	D₄	1	8	yes	complemented
114	C₂×C₄²×C₇	C₂³	1	2	yes	—
115	C₂×C₄²×C₇	C₂³	1	2	yes	—
116	C₂×C₄²×C₇	C₂³	1	2	yes	—
117	C₂×C₄²×C₇	C₂³	1	2	yes	—
118	C₂×C₄²×C₇	C₂³	1	2	yes	—
119	C₂×C₄²×C₇	C₂³	1	2	yes	—
120	C₂×C₄²×C₇	C₂³	1	2	yes	—
121	C₂×C₄²×C₇	C₂³	1	2	yes	—
122	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
123	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
124	C₂×C₄²×C₇	C₂³	1	2	yes	—
125	C₂×C₄²×C₇	C₂³	1	4	yes	—
126	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
129	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
130	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
131	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₇	C₂³	1	2	yes	—
133	C₇×#95	C₂³	1	8	yes	—
134	C₇×#95	C₂³	1	8	yes	—
135	C₇×#95	C₂³	1	8	yes	—
136	C₂×#529	C₂×C₇	1	2	yes	complemented
137	#2861	C₂×C₇	1	2	yes	complemented
138	#2860	C₂×C₇	1	4	yes	complemented
139	#2859	C₂×C₇	1	1	yes	characteristic, complemented
140	#2858	C₂×C₇	1	1	yes	characteristic, complemented
141	#2857	C₂×C₇	1	1	yes	characteristic, complemented
142	#2856	C₂×C₇	1	1	yes	characteristic
143	#2854	C₂×C₇	1	4	yes	complemented
144	#2850	C₂×C₇	1	2	yes	complemented
145	C₄×C₄⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
146	C₄×#127	C₂×C₇	1	1	yes	characteristic, complemented
147	C₄×#124	C₂×C₇	1	2	yes	complemented
148	C₄×#121	C₂×C₇	1	4	yes	complemented
149	#2293	C₂×C₇	1	4	yes	complemented
150	C₂×C₄³	C₂×C₇	1	1	yes	characteristic, complemented
151	C₂⁴×C₇	C₂⁴	1	4	yes	—
152	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
153	C₂×C₇×Q₈	—	2	4	no	—
154	C₂×C₇×Q₈	—	2	4	no	—
155	C₂×C₇×Q₈	—	2	4	no	—
156	C₂×C₇×D₄	—	2	8	no	—
157	C₂×C₇×D₄	—	2	16	no	—
158	C₂×C₇×D₄	—	2	4	no	—
159	C₂×C₇×D₄	—	2	8	no	—
160	C₂×C₇×D₄	—	2	8	no	—
161	C₂×C₇×D₄	—	2	4	no	—
162	C₂×C₇×D₄	—	2	8	no	—
163	C₂×C₇×D₄	—	2	4	no	—
164	C₂²×C₄×C₇	—	2	4	no	—
165	C₂²×C₄×C₇	—	2	4	no	—
166	C₂²×C₄×C₇	—	2	4	no	—
167	C₂²×C₄×C₇	—	2	4	no	—
168	C₂²×C₄×C₇	—	2	4	no	—
169	C₂²×C₄×C₇	—	2	4	no	—
170	C₂²×C₄×C₇	—	2	4	no	—
171	C₂²×C₄×C₇	—	2	2	no	—
172	C₂²×C₄×C₇	—	2	2	no	—
173	C₂²×C₄×C₇	—	2	8	no	—
174	C₂²×C₄×C₇	—	2	16	no	—
175	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
176	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
177	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
178	C₂²×C₄×C₇	#41	1	8	yes	—
179	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
180	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
181	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
182	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
183	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
184	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
185	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
186	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
187	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
188	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
189	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
190	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
191	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
192	C₇×C₄⋊C₄	—	2	8	no	—
193	C₇×C₄⋊C₄	—	2	8	no	—
194	C₇×C₄⋊C₄	—	2	4	no	—
195	C₇×C₄⋊C₄	—	2	8	no	—
196	C₇×C₄⋊C₄	—	2	4	no	—
197	C₇×C₄⋊C₄	—	2	8	no	—
198	C₇×C₄⋊C₄	—	2	8	no	—
199	C₇×C₄⋊C₄	—	2	8	no	—
200	C₇×C₄⋊C₄	—	2	8	no	—
201	C₇×C₂²⋊C₄	—	2	8	no	—
202	C₇×C₂²⋊C₄	—	2	8	no	—
203	C₇×C₂²⋊C₄	—	2	8	no	—
204	C₇×C₂²⋊C₄	—	2	8	no	—
205	C₇×C₂²⋊C₄	—	2	8	no	—
206	C₇×C₂²⋊C₄	—	2	16	no	—
207	C₇×C₂²⋊C₄	—	2	16	no	—
208	C₇×C₂²⋊C₄	—	2	16	no	—
209	C₄²×C₇	—	2	8	no	—
210	C₄²×C₇	—	2	4	no	—
211	C₄²×C₇	—	2	4	no	—
212	C₄²×C₇	—	2	4	no	—
213	C₄²×C₇	—	2	4	no	—
214	C₄²×C₇	—	2	4	no	—
215	C₄²×C₇	—	2	4	no	—
216	C₄²×C₇	—	2	4	no	—
217	C₄²×C₇	—	2	4	no	—
218	C₄²×C₇	—	2	4	no	—
219	C₄²×C₇	—	2	2	no	—
220	C₄²×C₇	—	2	2	no	—
221	C₄²×C₇	C₂×D₄	1	4	yes	—
222	C₄²×C₇	C₂×D₄	1	4	yes	—
223	C₄²×C₇	C₂×D₄	1	4	yes	—
224	C₄²×C₇	C₂×D₄	1	4	yes	—
225	C₄²×C₇	#41	1	8	yes	—
226	C₄²×C₇	#41	1	4	yes	—
227	C₄²×C₇	#41	1	4	yes	—
228	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
229	C₂×#127	C₂²×C₇	1	1	yes	characteristic
230	#529	—	2	16	no	—
231	C₂×#126	C₂²×C₇	1	4	yes	—
232	C₂×#125	C₂²×C₇	1	2	yes	—
233	C₂×#124	C₂²×C₇	1	2	yes	—
234	C₂×#124	C₂²×C₇	1	2	yes	—
235	C₂×#123	C₂²×C₇	1	4	yes	—
236	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
237	C₂×#121	C₂²×C₇	1	2	yes	—
238	C₂×#121	C₂²×C₇	1	4	yes	—
239	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
240	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
241	C₂×C₄×D₄	C₂²×C₇	1	4	yes	—
242	C₂×C₄×D₄	C₂²×C₇	1	4	yes	—
243	C₂×#117	C₂²×C₇	1	4	yes	—
244	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
245	C₂²×C₄²	C₂²×C₇	1	2	yes	—
246	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
247	C₂²×C₄²	C₂²×C₇	1	2	yes	—
248	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
249	#391	C₂²×C₇	1	2	yes	—
250	#391	C₂²×C₇	1	2	yes	—
251	#390	C₂²×C₇	1	2	yes	—
252	#390	C₂²×C₇	1	4	yes	—
253	#390	C₂²×C₇	1	4	yes	—
254	#390	C₂²×C₇	1	4	yes	—
255	#390	C₂²×C₇	1	2	yes	—
256	#390	C₂²×C₇	1	4	yes	—
257	#389	C₂²×C₇	1	4	yes	—
258	#389	C₂²×C₇	1	4	yes	—
259	#389	C₂²×C₇	1	4	yes	—
260	#389	C₂²×C₇	1	4	yes	—
261	#388	C₂²×C₇	1	8	yes	—
262	#388	C₂²×C₇	1	8	yes	—
263	#388	C₂²×C₇	1	8	yes	—
264	#388	C₂²×C₇	1	8	yes	—
265	#386	C₂²×C₇	1	8	yes	—
266	#384	C₂²×C₇	1	1	yes	characteristic
267	#384	C₂²×C₇	1	1	yes	characteristic
268	#382	C₂²×C₇	1	2	yes	—
269	#380	C₂²×C₇	1	4	yes	—
270	C₄×C₄⋊C₄	C₂²×C₇	1	4	yes	—
271	C₄×C₂²⋊C₄	C₂²×C₇	1	8	yes	—
272	C₄³	C₂²×C₇	1	1	yes	characteristic
273	C₄³	C₂²×C₇	1	1	yes	characteristic
274	C₄³	C₂²×C₇	1	2	yes	—
275	C₄³	C₂²×C₇	1	1	yes	characteristic
276	C₄³	C₂²×C₇	1	2	yes	—
277	C₄³	C₂²×C₇	1	1	yes	characteristic
278	C₂³×C₇	—	2	1	no	—
279	C₂³×C₇	—	2	2	no	—
280	C₂³×C₇	—	2	1	no	—
281	C₂³×C₇	—	2	4	no	—
282	C₂³×C₇	—	2	4	no	—
283	C₂³×C₇	—	2	8	no	—
284	C₂³×C₇	—	2	8	no	—
285	C₂³×C₇	—	2	4	no	—
286	C₂³×C₇	C₂²×D₄	1	2	yes	—
287	C₂³×C₇	C₂×#41	1	4	yes	—
288	C₂³×C₇	C₂⁵	1	1	yes	characteristic
289	C₇×Q₈	—	4	8	no	—
290	C₇×D₄	—	4	16	no	—
291	C₇×D₄	—	4	16	no	—
292	C₇×D₄	—	4	8	no	—
293	C₂×C₄×C₇	—	2	16	no	—
294	C₂×C₄×C₇	—	2	8	no	—
295	C₂×C₄×C₇	—	2	2	no	—
296	C₂×C₄×C₇	—	2	2	no	—
297	C₂×C₄×C₇	—	2	1	no	—
298	C₂×C₄×C₇	—	2	2	no	—
299	C₂×C₄×C₇	—	2	2	no	—
300	C₂×C₄×C₇	—	2	2	no	—
301	C₂×C₄×C₇	—	2	1	no	—
302	C₂×C₄×C₇	—	2	2	no	—
303	C₂×C₄×C₇	—	2	2	no	—
304	C₂×C₄×C₇	—	2	2	no	—
305	C₂×C₄×C₇	—	2	2	no	—
306	C₂×C₄×C₇	—	2	16	no	—
307	C₂×C₄×C₇	—	2	8	no	—
308	C₂×C₄×C₇	—	2	8	no	—
309	C₂×C₄×C₇	—	2	4	no	—
310	C₂×C₄×C₇	—	2	4	no	—
311	C₂×C₄×C₇	—	2	4	no	—
312	C₂×C₄×C₇	—	2	4	no	—
313	C₂×C₄×C₇	—	2	8	no	—
314	C₂×C₄×C₇	—	2	8	no	—
315	C₂×C₄×C₇	—	2	4	no	—
316	C₂×C₄×C₇	—	4	16	no	—
317	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
318	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
319	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
320	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
321	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
322	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
323	C₂×C₄×C₇	C₂×#41	1	4	yes	—
324	C₂×C₄×C₇	C₂×#41	1	4	yes	—
325	C₂×C₄×C₇	C₂×#41	1	4	yes	—
326	C₂×C₄×C₇	C₂×#41	1	4	yes	—
327	C₂×C₄×C₇	C₂×#41	1	4	yes	—
328	C₂×C₄×C₇	C₂×#41	1	4	yes	—
329	C₂×C₄×C₇	C₂×#41	1	4	yes	—
330	C₂×C₄×C₇	C₂×#41	1	2	yes	—
331	C₂×C₄×C₇	C₂×#41	1	2	yes	—
332	C₂²×Q₈	C₂³×C₇	1	2	yes	—
333	C₂²×D₄	C₂³×C₇	1	4	yes	—
334	C₂²×D₄	C₂³×C₇	1	2	yes	—
335	C₂²×D₄	C₂³×C₇	1	4	yes	—
336	C₂³×C₄	C₂³×C₇	1	4	yes	—
337	C₂³×C₄	C₂³×C₇	1	2	yes	—
338	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
339	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
340	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
341	C₂³×C₄	C₂³×C₇	1	2	yes	—
342	C₄⋊Q₈	—	2	4	no	—
343	#127	—	2	4	no	—
344	#126	—	2	16	no	—
345	#125	—	2	8	no	—
346	#124	—	2	8	no	—
347	#124	—	2	8	no	—
348	#123	—	2	16	no	—
349	C₂²⋊Q₈	—	2	8	no	—
350	#121	—	2	8	no	—
351	#121	—	2	16	no	—
352	C₄×Q₈	—	2	8	no	—
353	C₄×D₄	—	2	16	no	—
354	C₄×D₄	—	2	8	no	—
355	C₄×D₄	—	2	16	no	—
356	#117	—	2	16	no	—
357	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
358	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
359	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
360	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
361	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
362	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
363	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
364	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
365	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
366	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
367	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
368	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
369	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
370	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
371	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
372	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
373	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
374	C₂×C₄²	—	2	8	no	—
375	C₂×C₄²	—	2	8	no	—
376	C₂×C₄²	—	2	4	no	—
377	C₂×C₄²	—	2	4	no	—
378	C₂×C₄²	C₇×D₄	1	8	yes	complemented
379	C₂×C₄²	C₂³×C₇	1	4	yes	—
380	C₂×C₄²	C₂³×C₇	1	2	yes	—
381	C₂×C₄²	C₂³×C₇	1	2	yes	—
382	C₂×C₄²	C₂³×C₇	1	2	yes	—
383	C₂×C₄²	C₂³×C₇	1	2	yes	—
384	C₂×C₄²	C₂³×C₇	1	2	yes	—
385	C₂×C₄²	C₂³×C₇	1	2	yes	—
386	C₂×C₄²	C₂³×C₇	1	2	yes	—
387	C₂×C₄²	C₂³×C₇	1	2	yes	—
388	C₂×C₄²	C₂³×C₇	1	2	yes	—
389	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
390	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
391	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
392	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
393	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
394	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
395	C₂×C₄²	C₂³×C₇	1	2	yes	—
396	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
397	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
398	#95	C₂³×C₇	1	8	yes	—
399	#95	C₂³×C₇	1	8	yes	—
400	#95	C₂³×C₇	1	8	yes	—
401	C₂²×C₇	—	2	4	no	—
402	C₂²×C₇	—	2	2	no	—
403	C₂²×C₇	—	2	2	no	—
404	C₂²×C₇	—	2	4	no	—
405	C₂²×C₇	—	4	8	no	—
406	C₂²×C₇	—	4	4	no	—
407	C₂²×C₇	—	4	4	no	—
408	C₂²×C₇	—	4	4	no	—
409	C₂²×C₇	—	4	8	no	—
410	C₂²×C₇	#532	1	4	yes	—
411	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
412	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
413	C₂²×C₇	C₂²×#41	1	2	yes	—
414	C₂²×C₇	C₂²×#41	1	2	yes	—
415	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
416	C₄×C₇	—	2	4	no	—
417	C₄×C₇	—	2	2	no	—
418	C₄×C₇	—	2	2	no	—
419	C₄×C₇	—	2	2	no	—
420	C₄×C₇	—	2	2	no	—
421	C₄×C₇	—	2	4	no	—
422	C₄×C₇	—	2	4	no	—
423	C₄×C₇	—	4	4	no	—
424	C₄×C₇	—	4	4	no	—
425	C₄×C₇	—	4	4	no	—
426	C₄×C₇	#529	1	8	yes	complemented
427	C₄×C₇	#532	1	4	yes	—
428	C₄×C₇	#532	1	4	yes	—
429	C₂⁴	C₂⁴×C₇	1	4	yes	—
430	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
431	C₂×Q₈	—	2	4	no	—
432	C₂×Q₈	—	2	4	no	—
433	C₂×Q₈	—	2	4	no	—
434	C₂×D₄	—	2	8	no	—
435	C₂×D₄	—	2	16	no	—
436	C₂×D₄	—	2	4	no	—
437	C₂×D₄	—	2	8	no	—
438	C₂×D₄	—	2	8	no	—
439	C₂×D₄	—	2	4	no	—
440	C₂×D₄	—	2	8	no	—
441	C₂×D₄	—	2	4	no	—
442	C₂²×C₄	—	2	4	no	—
443	C₂²×C₄	—	2	4	no	—
444	C₂²×C₄	—	2	4	no	—
445	C₂²×C₄	—	2	4	no	—
446	C₂²×C₄	—	2	4	no	—
447	C₂²×C₄	—	2	4	no	—
448	C₂²×C₄	—	2	4	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	8	no	—
452	C₂²×C₄	—	2	16	no	—
453	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
454	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
455	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
456	C₂²×C₄	C₇×#41	1	8	yes	—
457	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
458	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
459	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
460	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
461	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
462	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
463	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
464	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
465	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
466	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
467	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
468	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
469	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
470	C₄⋊C₄	—	2	8	no	—
471	C₄⋊C₄	—	2	8	no	—
472	C₄⋊C₄	—	2	4	no	—
473	C₄⋊C₄	—	2	8	no	—
474	C₄⋊C₄	—	2	4	no	—
475	C₄⋊C₄	—	2	8	no	—
476	C₄⋊C₄	—	2	8	no	—
477	C₄⋊C₄	—	2	8	no	—
478	C₄⋊C₄	—	2	8	no	—
479	C₂²⋊C₄	—	2	8	no	—
480	C₂²⋊C₄	—	2	8	no	—
481	C₂²⋊C₄	—	2	8	no	—
482	C₂²⋊C₄	—	2	8	no	—
483	C₂²⋊C₄	—	2	8	no	—
484	C₂²⋊C₄	—	2	16	no	—
485	C₂²⋊C₄	—	2	16	no	—
486	C₂²⋊C₄	—	2	16	no	—
487	C₄²	—	2	8	no	—
488	C₄²	—	2	4	no	—
489	C₄²	—	2	4	no	—
490	C₄²	—	2	4	no	—
491	C₄²	—	2	4	no	—
492	C₄²	—	2	4	no	—
493	C₄²	—	2	4	no	—
494	C₄²	—	2	4	no	—
495	C₄²	—	2	4	no	—
496	C₄²	—	2	4	no	—
497	C₄²	—	2	2	no	—
498	C₄²	—	2	2	no	—
499	C₄²	C₂×C₇×D₄	1	4	yes	—
500	C₄²	C₂×C₇×D₄	1	4	yes	—
501	C₄²	C₂×C₇×D₄	1	4	yes	—
502	C₄²	C₂×C₇×D₄	1	4	yes	—
503	C₄²	C₇×#41	1	8	yes	—
504	C₄²	C₇×#41	1	4	yes	—
505	C₄²	C₇×#41	1	4	yes	—
506	C₂×C₇	—	2	4	no	—
507	C₂×C₇	—	8	4	no	—
508	C₂×C₇	C₂×#529	1	2	yes	—
509	C₂×C₇	C₂×#532	1	1	yes	characteristic
510	C₂×C₇	C₂×#532	1	1	yes	characteristic
511	C₂×C₇	C₂×#532	1	1	yes	characteristic
512	C₂×C₇	#3444	1	2	yes	—
513	C₂³	—	2	1	no	—
514	C₂³	—	2	2	no	—
515	C₂³	—	2	1	no	—
516	C₂³	—	2	4	no	—
517	C₂³	—	2	4	no	—
518	C₂³	—	2	8	no	—
519	C₂³	—	2	8	no	—
520	C₂³	—	2	4	no	—
521	C₂³	C₂²×C₇×D₄	1	2	yes	—
522	C₂³	C₂×C₇×#41	1	4	yes	—
523	C₂³	C₂⁵×C₇	1	1	yes	characteristic
524	Q₈	—	4	8	no	—
525	D₄	—	4	16	no	—
526	D₄	—	4	16	no	—
527	D₄	—	4	8	no	—
528	C₂×C₄	—	2	16	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	8	no	—
541	C₂×C₄	—	2	16	no	—
542	C₂×C₄	—	2	8	no	—
543	C₂×C₄	—	2	8	no	—
544	C₂×C₄	—	2	4	no	—
545	C₂×C₄	—	2	4	no	—
546	C₂×C₄	—	2	4	no	—
547	C₂×C₄	—	2	4	no	—
548	C₂×C₄	—	2	8	no	—
549	C₂×C₄	—	2	8	no	—
550	C₂×C₄	—	2	4	no	—
551	C₂×C₄	—	4	16	no	—
552	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
553	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
554	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
555	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
556	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
557	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
558	C₂×C₄	C₂×C₇×#41	1	4	yes	—
559	C₂×C₄	C₂×C₇×#41	1	4	yes	—
560	C₂×C₄	C₂×C₇×#41	1	4	yes	—
561	C₂×C₄	C₂×C₇×#41	1	4	yes	—
562	C₂×C₄	C₂×C₇×#41	1	4	yes	—
563	C₂×C₄	C₂×C₇×#41	1	4	yes	—
564	C₂×C₄	C₂×C₇×#41	1	4	yes	—
565	C₂×C₄	C₂×C₇×#41	1	2	yes	—
566	C₂×C₄	C₂×C₇×#41	1	2	yes	—
567	C₇	#36631	1	1	yes	characteristic, direct product factor, Sylow
568	C₂²	—	2	4	no	—
569	C₂²	—	2	2	no	—
570	C₂²	—	2	2	no	—
571	C₂²	—	2	4	no	—
572	C₂²	—	4	8	no	—
573	C₂²	—	4	4	no	—
574	C₂²	—	4	4	no	—
575	C₂²	—	4	4	no	—
576	C₂²	—	4	8	no	—
577	C₂²	C₇×#532	1	4	yes	—
578	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
579	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
580	C₂²	C₂²×C₇×#41	1	2	yes	—
581	C₂²	C₂²×C₇×#41	1	2	yes	—
582	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
583	C₄	—	2	4	no	—
584	C₄	—	2	2	no	—
585	C₄	—	2	2	no	—
586	C₄	—	2	2	no	—
587	C₄	—	2	2	no	—
588	C₄	—	2	4	no	—
589	C₄	—	2	4	no	—
590	C₄	—	4	4	no	—
591	C₄	—	4	4	no	—
592	C₄	—	4	4	no	—
593	C₄	C₇×#529	1	8	yes	complemented
594	C₄	C₇×#532	1	4	yes	—
595	C₄	C₇×#532	1	4	yes	—
596	C₂	—	2	4	no	—
597	C₂	—	8	4	no	—
598	C₂	C₂×C₇×#529	1	2	yes	—
599	C₂	C₂×C₇×#532	1	1	yes	characteristic
600	C₂	C₂×C₇×#532	1	1	yes	characteristic
601	C₂	C₂×C₇×#532	1	1	yes	characteristic
602	C₂	C₇×#3444	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇
socle	C₂³×C₇	C₂⁵
prime radical	C₇×#2856	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₇ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×C₇×#529	C₂	semidirect
2. C₇×#2861	C₂	semidirect
3. C₇×#2860	C₂	semidirect
4. C₇×#2859	C₂	semidirect
5. C₇×#2858	C₂	semidirect
6. C₇×#2857	C₂	semidirect
8. C₇×#2854	C₂	semidirect
9. C₇×#2850	C₂	semidirect
10. C₄×C₇×C₄⋊Q₈	C₂	semidirect
11. C₄×C₇×#127	C₂	semidirect
12. C₄×C₇×#124	C₂	semidirect
13. C₄×C₇×#121	C₂	semidirect
14. C₇×#2293	C₂	semidirect
15. C₂×C₄³×C₇	C₂	semidirect
66. #36631	C₇	direct (N × H)
113. C₂×C₄²×C₇	D₄	semidirect
136. C₂×#529	C₂×C₇	semidirect
137. #2861	C₂×C₇	semidirect
138. #2860	C₂×C₇	semidirect
139. #2859	C₂×C₇	semidirect
140. #2858	C₂×C₇	semidirect
141. #2857	C₂×C₇	semidirect
143. #2854	C₂×C₇	semidirect
144. #2850	C₂×C₇	semidirect
145. C₄×C₄⋊Q₈	C₂×C₇	semidirect
146. C₄×#127	C₂×C₇	semidirect
147. C₄×#124	C₂×C₇	semidirect
148. C₄×#121	C₂×C₇	semidirect
149. #2293	C₂×C₇	semidirect
150. C₂×C₄³	C₂×C₇	semidirect
378. C₂×C₄²	C₇×D₄	semidirect
426. C₄×C₇	#529	semidirect
567. C₇	#36631	direct (N × H)
593. C₄	C₇×#529	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₇×#529	2
C₇×#2861	2
C₇×#2860	2
C₇×#2859	2
C₇×#2858	2
C₇×#2857	2
C₇×#2856	2
C₇×#2854	2
C₇×#2850	2
C₄×C₇×C₄⋊Q₈	2
C₄×C₇×#127	2
C₄×C₇×#124	2
C₄×C₇×#121	2
C₇×#2293	2
C₂×C₄³×C₇	2
#36631	7

Subgroups — C7×#36631 #13213847

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#36631 #13213847